Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import bisect
def solve():
    n = input()
    SUM = []
    SUM.append(1)
    s = 1
    i = 1
    while s < n:
        s = s + (i+1)
        SUM.append(s)
        i += 1
    SUM_len = len(SUM)
    for i in range(SUM_len):
        x = SUM[i]
        y = n - x
        pos = bisect.bisect_left(SUM, y)
        if pos != SUM_len and SUM[pos] == y:
            return "YES"
    return "NO"


print solve()